View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Discrete Mathematics 299 (2005) 269–287 www.elsevier.com/locate/disc Brian Alspach and his workଁ Joy Morrisa, Mateja Šajnab aDepartment of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB, Canada T1K 3M4 bDepartment of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, Ont. Canada K1N 6N5 Received 28 February 2005; received in revised form 9 March 2005; accepted 11 March 2005 Available online 26 July 2005 Abstract This article provides an overview of the life and work of Brian Alspach, including a complete list of his mathematical publications (to date). © 2005 Elsevier B.V. All rights reserved. Keywords: Alspach; Brian Alspach; Tournaments; Permutation groups; Graphs; Decompositions; Factorizations; Hamilton cycles; Biography 0. Introduction It’s hard to think of Brian Alspach these days, without conjuring up a mental picture of feet in Birkenstocks, and his Australian hat within arm’s reach, if not perched on his head. Often, a briefcase will be stashed nearby, if he isn’t actually carrying it. These outward symbols are accurate reflections of Brian’s character.Although his outlook is casual and laid-back, his attention rarely strays far from his passions in life, which include the work that is stored in that briefcase. ଁ This research was supported in part by the Natural Sciences and Engineering Research Council of Canada. E-mail addresses: [email protected] (J. Morris),[email protected] (M. Šajna). 0012-365X/$ - see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.disc.2005.03.024 270 J. Morris, M. Šajna / Discrete Mathematics 299 (2005) 269–287 Brian’s 65th birthday, on May 29, 2003, was celebrated at the “Graph Theory of Brian Alspach” conference, held at Simon Fraser University (SFU) in Vancouver (where he spent most of his career). This volume of papers forms the proceedings of the conference. The conference banquet provided a rare opportunity for Brian’s colleagues, collaborators, and students, as well as friends and family members to get together, and to share stories about Brian. The guests were delightfully entertained by the “BrianAlspach Quiz” prepared for the occasion by Brooks Reid, who served as the Master of Ceremonies. Brooks has graciously allowed us to include some of his quiz questions in this paper. We are happy to share them with you. Answers either appear with the questions, or can be found in the text. Brian Alspach has been a tremendous influence in the mathematical community. He enjoys meeting young mathematicians, and at conferences, is often to be found at the center of a very lively group. He is a talented mentor, with a knack for encouraging young people. Even a brief meeting with him has proven influential in numerous careers, but Brian has no hesitation in going far out of his way to provide further encouragement.A substantial amount of his grant money goes toward supporting students—not only his own—with funding to attend conferences or to visit other researchers. He has also regularly provided financial assistance to researchers who want to visit and work with him. His home is often opened to visitors who are at various stages of their careers, but particularly to students and to mathematicians who are still establishing themselves. Brian’s example and leadership have set the standards for collaborative research, not only among those mathematicians whom he has mentored directly, but among all of those who work in the areas where his research has been influential. In general, these areas of research do not have the cut-throat attitude that is too often seen in the scientific community. Instead, credit for results is shared generously, and assistance is offered freely. This is certainly Brian’s own approach. He has collaborated with almost 60 different co-authors. Brian maintains a keen interest in applications of mathematics, particularly those in industry, which he feels are an important part of maintaining young adults’interest in math- ematics. He keeps abreast of research in areas beyond mathematics, and has published papers about applications of mathematics. He maintains contacts in industry, has done con- sulting work, and has led industry-funded projects. He provided the energy and leadership that recently led to the foundation of an industrial mathematics program at Simon Fraser University, as well as having founded and served as the Coordinator for the related Mas- ter’s of Management and Systems Science program for many years. Brian was also one of the founders of the co-op education program at SFU; his role included championing the program through resistance at the University Senate. (In co-operative education, universi- ties work with employers to provide students with alternating semesters of study and job experience; the program at SFU is now one of the longest-standing and most respected in Canada.) Question 1. Brian was, at one time, an avid: Question 2. Brian is an ardent fan of: (a) fisherman (a) Saskatchewan Roughriders football (b) skier (b) U. Washington Husky football (c) horse shoer (c) San Diego Padres baseball (d) golfer (d) New Westminster Salmonbellies Box lacrosse J. Morris, M. Šajna / Discrete Mathematics 299 (2005) 269–287 271 (e) softball player (e) New Zealand All-Blacks rugby (f) curler (f) B.C. Lions football It would be remiss to write much about Brian without mentioning ways in which he combines the passions in his life, and uses his other interests to popularise mathematics. He enjoys giving talks to the public and to school groups, and when doing so, he often uses either sports or games to introduce mathematical problems in an interesting way. He has a great interest in both football (specifically, the Washington Huskies), and baseball. Besides being a fan of the Seattle Mariners baseball team, he played on fast pitch softball teams in leagues around the Vancouver area for many years. More recently, his enjoyment of poker has led him to writing regular articles in popular poker magazines, about the mathematics behind various situations in that game. He has also done consulting work in the gaming industry. This paper consists of a brief overview of Brian’s life, followed by discussions of some of the areas in which he has made significant research contributions. At the end of this paper is a complete list of his publications. Brian was born on May 29, 1938, in North Dakota. By the time he was 9 years old, his family had settled in Seattle, Washington. He has one brother, Neal, and one sister, Diane, both of whom live in the Seattle area, where his mother also still resides. After finishing his undergraduate degree at the University of Washington in 1961, Brian moved to California, where he undertook graduate work at the University of California–Santa Barbara. He maintained a keen interest in the Washington Huskies college football team, and had season tickets to their home games for years. When living in Vancouver, he would drive down to Seattle regularly to watch their games, and would occasionally travel to attend road games. Brian taught one year (1961–1962) of junior high school between his B.A. and his Ph.D. Question 3. Before settling into Cayley graphs, Question 4. Brian’s earliest decompositions, automorphisms, etc. published paper appeared in Brian worked in: what year? (a) Ramsey theory (a) 1965 (b) enumeration (b) 1967 (c) tournaments (c) 1968 (d) reconstruction (d) 1969 (e) matroids (e) 1970 (f) divinity (f) 1938 Brian’s graduate work was done under the supervision of Paul Kelly, in a department that was very strong in the area of linear algebra. Kelly is given joint credit with Ulam for posing the famous Graph Reconstruction Conjecture, and established the result for trees. Brian completed his M.A. at UCSB in 1964, and his Ph.D. in 1966; the title of his thesis was “A Class of Tournaments.” Brian moved to Vancouver in 1966, where he joined Simon Fraser University’s Depart- ment of Mathematics and Statistics one year after the university was founded. During his career there, he was influential at a wide variety of levels, from the local to the interna- 272 J. Morris, M. Šajna / Discrete Mathematics 299 (2005) 269–287 tional. He sat on editorial boards of journals, helped to organise international conferences and workshops, and wrote many Math Reviews. Question 5. Brian was a host for the Question 6. Brian “Cycles in Graphs”8-week summer was a problem workshop/conference at SFU in: editor for (a) 1982 (a) Discrete Mathematics (b) 1980 (b) Journal of Comb. Theory (c) 1978 (c) Journal of Graph Theory (d) 1986 (d) Bulletin of the Canadian Math. Soc. (e) 1984 (e) Spectrum (f) 1988 (f) Backgammon Today Answers. The highly successful “Cycles in Graphs” workshop, organised by Brian and Pavol Hell, took place in 1982. It included very generous time for work and collaboration. The proceedings were edited by Brian, with Chris Godsil, and appeared as a volume in Annals of Discrete Math. Brian also contributed many open problems to Discrete Mathematics. At a regional level, he helped to found, and was the main coordinator for the West Coast “Combinatorial Potlatches,” from their origins in the 1970s, until 1997. These one-day gatherings, held once or twice a year, bring together combinatorial researchers and students from around the Pacific Northwest, to discuss their research interests and to get to know one another. Locally, he organised and coordinated seminars, mentored students, and participated in many projects to raise awareness of mathematics in the community. By the late 1970s, the graduate program in discrete mathematics at SFU had grown to the point where Brian decided it was worthwhile to institute an instructional seminar series.